General Values of Inverse Trigonometric Functions

We will learn how to find the general values of inverse trigonometric functions in different types of problems.

1. Find the general values of sinβˆ’1 (- √3/2)

Solution:  

Let, sinβˆ’1 (- √3/2) = ΞΈ

Therefore, sin θ = - √3/2

β‡’ sin ΞΈ = - sin (Ο€/3)

β‡’ sin ΞΈ = (- Ο€/3)

Therefore, the general value of sinβˆ’1 (- √3/2) = ΞΈ = nΟ€ - (- 1)n Ο€/3, where, n = 0 or any integer.

2. Find the general values of cotβˆ’1 (- 1)

Solution:

Let, cotβˆ’1 (- 1) = ΞΈ                    

Therefore, cot ΞΈ = - 1

β‡’ cot ΞΈ = cot (- Ο€/4)

Therefore, the general value of cotβˆ’1 (- 1) = ΞΈ = nΟ€ - Ο€/4, where, n = 0 or any integer.

 

3. Find the general values of cosβˆ’1 (1/2)      

Solution:   

Let, cosβˆ’1 1/2 = ΞΈ           

Therefore, cos ΞΈ = 1/2

β‡’ cos ΞΈ = cos (Ο€/3)

Therefore, the general value of cosβˆ’1 (1/2) = ΞΈ = 2nΟ€ Β± Ο€/3, where, n = 0 or any integer.

 

4. Find the general values of secβˆ’1 (- 2)  

Solution:

Let, secβˆ’1 (- 2) = ΞΈ

Therefore, sec ΞΈ = - 2

β‡’ sec ΞΈ = - sec (Ο€/3)

β‡’ sec ΞΈ = sec (Ο€ - Ο€/3)

β‡’ sec ΞΈ = sec (2Ο€/3)

Therefore, the general value of secβˆ’1 (- 2) = ΞΈ = 2nΟ€ Β± 2Ο€/3, where, n = 0 or any integer.

 

5. Find the general values of cscβˆ’1 (√2)

Solution:

Let, cscβˆ’1 (√2) = ΞΈ           

Therefore, csc θ = √2 .

β‡’csc ΞΈ = csc (Ο€/4)

Therefore, the general value of cscβˆ’1 (√2 ) = ΞΈ = nΟ€ + (- 1)n Ο€/4, where, n = 0 or any integer.

 

6. Find the general values of tanβˆ’1 (√3)

Solution:

 Let, tanβˆ’1 (√3) = ΞΈ                   

Therefore, tan θ = √3

β‡’ tan ΞΈ = tan (Ο€/3)

Therefore, the general value of tanβˆ’1 (√3) = ΞΈ = nΟ€ + Ο€/3 where, n = 0 or any integer.

● Inverse Trigonometric Functions






11 and 12 Grade Math

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